scholarly journals On Some Boundedness and Convergence Properties of a Class of Switching Maps in Probabilistic Metric Spaces with Applications to Switched Dynamic Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-14
Author(s):  
M. De la Sen ◽  
A. Ibeas
Keyword(s):  
Fixed Point ◽  
Dynamic Systems ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
The Self ◽  
Convergence Properties ◽  
Probabilistic Metric Spaces ◽  
Switching Law ◽  
Probabilistic Metric

This paper investigates some boundedness and convergence properties of sequences which are generated iteratively through switched mappings defined on probabilistic metric spaces as well as conditions of existence and uniqueness of fixed points. Such switching mappings are built from a set of primary self-mappings selected through switching laws. The switching laws govern the switching process in between primary self-mappings when constructing the switching map. The primary self-mappings are not necessarily contractive but if at least one of them is contractive then there always exist switching maps which exhibit convergence properties and have a unique fixed point. If at least one of the self-mappings is nonexpansive or an appropriate combination given by the switching law is nonexpansive, then sequences are bounded although not convergent, in general. Some illustrative examples are also given.

Fixed point theorems in probabilistic metric spaces using property (E.A)

2013 ◽  
Vol 17 (2) ◽  
pp. 11-24
Author(s):  
Badridatt Pant ◽  
Brian Fisher ◽  
Sunny Chauhan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Probabilistic Metric Spaces ◽  
Probabilistic Metric

scholarly journals Some Fixed Point Theorems in Generalized Probabilistic Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Chuanxi Zhu ◽  
Wenqing Xu ◽  
Zhaoqi Wu
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Probabilistic Metric Spaces ◽  
Contraction Mappings ◽  
Probabilistic Metric

We introduce the concepts of(H,ψ,Φ)-contraction and probabilistic(α,φ)-contraction mappings in generalized probabilistic metric spaces and prove some fixed point theorems for such two types of mappings in generalized probabilistic metric spaces. Our results generalize and extend many comparable results in existing literature. Some examples are also given to support our results. Finally, an application to the existence of solutions for a class of integral equations is presented by utilizing one of our main results.

scholarly journals Common fixed point theorems in complete metric and probabilistic metric spaces

1987 ◽  
Vol 36 (1) ◽  
pp. 73-88 ◽  
Author(s):  
Mila Stojakovic
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Probabilistic Metric Spaces ◽  
Continuous Mappings ◽  
Contraction Condition ◽  
Probabilistic Metric ◽  
Common Fixed Point Theorems

In this paper several common fixed point theorems for four continuous mappings in Menger and metric spaces are proved. These mappings are assumed to satisfy some generalizations of the contraction condition.

scholarly journals Fixed point theorems in modular G-metric spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Godwin Amechi Okeke ◽  
Daniel Francis ◽  
Manuel de la Sen ◽  
Mujahid Abbas
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Weakly Compatible ◽  
Special Cases

AbstractWe prove the existence and uniqueness of fixed points of some generalized contractible operators defined on modular G-metric spaces and also prove the modular G-continuity of such operators. Furthermore, we prove that some generalized weakly compatible contractive operators in modular G-metric spaces have a unique fixed point. Our results extend, generalize, complement and include several known results as special cases.

scholarly journals On ψ-contractions and common fixed point results in probabilistic metric spaces

2020 ◽  
Vol 21 (1) ◽  
pp. 319-338
Author(s):  
Jingfeng Tian ◽  
◽  
Ximei Hu ◽  
Donal O'Regan ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Probabilistic Metric Spaces ◽  
Probabilistic Metric
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